Automatic particular solutions of arbitrary high-order splines associated with polyharmonic and poly-Helmholtz equations

DOI10.1016/j.enganabound.2011.02.005zbMath1259.65197OpenAlexW1977163374MaRDI QIDQ1944556

Chia-Cheng Tsai

Publication date: 25 March 2013

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2011.02.005

zbMATH Keywords

radial basis functiondual reciprocity methodmethod of fundamental solutionspolyharmonic equationautomatic particular solutionpoly-Helmholtz equation

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Related Items (7)

Generalized polyharmonic multiquadrics ⋮ Compactly supported radial basis functions for solving certain high order partial differential equations in 3D ⋮ The MFS as a basis for the PIM or the HAM -- comparison of numerical methods ⋮ Fast method of approximate particular solutions using Chebyshev interpolation ⋮ Degenerate kernels of polyharmonic and poly-Helmholtz operators in polar and spherical coordinates ⋮ Multiquadric and Chebyshev approximation to three-dimensional thermoelasticity with arbitrary body forces ⋮ Homotopy method of fundamental solutions for solving certain nonlinear partial differential equations

Uses Software

• MPFR

Cites Work

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• The method of fundamental solutions for oscillatory and porous buoyant flows
• Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operators
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• A new approach to free vibration analysis using boundary elements
• Fast and accurate computation of Bessel functions with (large) complex order and argument
• A modified Kirchhoff theory for boundary element bending analysis of thin plates
• On the smoothness of positive definite and radial functions
• Radial basis function approximation in the dual reciprocity method
• Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions
• Particular solutions of Helmholtz-type operators using higher order polyharmonic splines
• Particular solutions of the multi-Helmholtz-type equation
• Heritage and early history of the boundary element method
• The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings
• Particular Solutions of Chebyshev Polynomials for Polyharmonic and Poly-Helmholtz Equations
• MPFR
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Polynomial particular solutions for certain partial differential operators
• The method of fundamental solutions for non‐linear thermal explosions
• Approximation of multivariate functions and evaluation of particular solutions using Chebyshev polynomial and trigonometric basis functions
• Solutions of slow Brinkman flows using the method of fundamental solutions
• BEM for thermoelasticity and elasticity with body force -- a revisit

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